1. North Dakota State University Fargo, ND 58108 USA
Extension Study on Item-Based P-Tree Collaborative Filtering for the Netflix Prize
Tingda Lu, Yan Wang, William Perrizo, Gregory Wettstein, Amal S. Perera
Computer Science
North Dakota State University Fargo, ND USA

2. Agenda
Introduction to the Recommendation Systems and Collaborative Filtering
P-Trees
Item-based P-Tree CF algorithm
Similarity measurements
Experimental results
Conclusion

3. Recommendation System
analyzes customer’s purchase (or rental) history
and identifies customer’s satisfaction ratings
recommends the most likely satisfying next purchases (rentals)
increases customer satisfaction
eventually leads to business success
Add some examples

4. Amazon.com Book Recommendations
amazon.com doesn’t know me,
generic recommendations
Make purchases, click items, rate items and make lists,
recommendations get “better”
Collaborative filtering
similar users like similar things
More choice necessitates better filters
Recommendation engines

5. Netflix Movie Recommendation
“The Netflix Prize seeks to substantially improve the accuracy of predictions about how much someone is going to love a movie based on previous ratings.”
$1 million prize was given last Fall to Belcore team for a >10% improvement over Netflix’s current movie recommender, Cinematch

6. Collaborative Filtering
Collaborative Filtering (CF) algorithm is widely used in recommender systems
User-based CF algorithm is limited because of its computation complexity
Item-based CF has fewer scalability concerns

7. P-Tree
P-Tree is a lossless, compressed, and data-mining-ready vertical data structure
P-trees are used for fast computation of counts and for masking specific phenomena
Data is first converted to P-trees

8. But it is pure (pure0) so this branch ends
Predicate tree technology: vertically project each attribute,
Current practice: Structure data into horizontal records. Process vertically (scans)
then vertically project each bit position of each attribute,
then compress each bit slice into a basic Ptree.
e.g., compression of R11 into P11 goes as follows:
Base 2
Base 10
R(A1 A2 A3 A4)
R[A1] R[A2] R[A3] R[A4] =
Horizontally structured
records
Scanned vertically
R11 1
R11 R12 R13 R21 R22 R23 R31 R32 R33 R41 R42 R43
pure1? false=0
pure1? true=1
Top-down construction of the 1-dimensional Ptree representation of R11, denoted, P11, is built by recording the truth of the universal predicate pure 1 in a tree recursively on halves (1/21 subsets), until purity is achieved.
pure1? false=0
pure1? false=0
pure1? false=0
Horizontally AND basic Ptrees
1. Whole is pure1? false  0
0 0
0 1
P11
P11 P12 P13 P21 P22 P23 P31 P32 P33 P41 P42 P43
0 0
0 1 1
1 0
1 0 01
0 1
0 0 ^
2. Left half pure1? false  0
3. Right half pure1? false  0
0 0
P11
5. Rt half of right half? true1
0 0
0 1
4. Left half of rt half ? false0
0 0
But it is pure (pure0) so this branch ends

9. P-Tree API size() Get size of PTree get_count() Get bit count of PTree
setbit()
Set a single bit of PTree
reset()
Clear the bits of PTree
&
AND operation of PTree |
OR operation of PTree ~
NOT operation of PTree
dump()
Print the binary representation of PTree
load_binary()
Load the binary representation of PTree

10. Item-based P-Tree CF PTree.load_binary(); // Calculate the similarity
while i in I {
while j in I {
simi,j = sim(PTree[i], Ptree[j]); }
// Get the top K nearest neighbors to item i
pt=Ptree.get_items(u);
sort(pt.begin(), pt.end(), simi,pt.get_index());
// Prediction of rating on item i by user u
sum = 0.0, weight = 0.0;
for (j=0; j<K; ++j) {
sum += ru,pt[j] * simi,pt[j];
weight += simi,pt[j];
pred = sum/weight

11. Item-Based Similarity (I)
Cosine based
Pearson correlation

12. Item-Based Similarity (II)
Adjusted Cosine
SVD item-feature

13. Similarity Correction
Two items are not similar if only a few customers purchased or rated both
We include the co-support in item similarity

14. Prediction
Weighted Average
Item Effects

15. RMSE on Neighbor Size Cosine Pearson Adj. Cos SVD IF K=10 1.0742
1.0092
0.9786
0.9865
K=20
1.0629
1.0006
0.9685
0.9900
K=30
1.0602
1.0019
0.9666
0.9972
K=40
1.0592
1.0043
0.9960
1.0031
K=50
1.0589
1.0064
0.9658
1.0078

16. Neighbor Size

17. Similarity Algorithm

18. Analysis Adjusted Cosine similarity algorithm gets much lower RMSE
The reason lies in the fact that other algorithms do not exclude based on user rating variance
Adjusted Cosine based algorithm discards users with high variance hence gets better prediction accuracy

19. Similarity Correction
All algorithms get better RMSE with similarity correction except Adjusted Cosine.
Cosine
Pearson
Adj. Cos
SVD IF
Before
1.0589
1.0006
0.9658
0.9865
After
1.0588
0.9726
1.0637
0.9791
Improve
0.009%
2.798% %
0.750%

20. Item Effects Improves rmse for all algorithms. Cosine Pearson Adj. Cos
SVD IF
Before
1.0589
1.0006
0.9658
0.9865
After
0.9450
0.9468
0.9381
Improve
9.576%
5.557%
1.967%
4.906%

21. Conclusion
Experiments were carried out on Cosine, Pearson, Adjusted Cosine and SVD item-feature algorithms.
Support corrections and item effects significantly improve the prediction accuracy.
Pearson and SVD item-feature algorithms achieve better results when similarity correction and item effects are included.

22. Questions and Comments?